In Harry Potter, no one believes Prof. Trelawney's predictions. The reason has to do with Greek Mythology!
In the Harry Potter books, Sybill Trelawney is a teacher of Divination at Hogwarts. Divination is to tell the future, but everyone thinks she is a fraud. While she makes some erroneous predictions (usually about a student dying), she can make accurate predictions when she goes into a trance.
However, there is a historical reason for why everyone thinks she's a fraud and it has to do with Greek Mythology. In the 5th Harry Potter book, it's said that Prof. Trelawney is the descendant of the great seer Cassandra Trelawney. While it might seem like a throwaway line, it probably refers to the Greek prophet Cassandra.
In the Greek story, the god Apollo fell in love with Cassandra and gave her the gift of prophecy. He then tried to put the moves on her and she rebuked him. He got angry and instead of taking the gift back, he cursed her: nobody would believe her predictions or the predictions of her descendants.